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Q. No.A uniform rod of mass \(m,\) having cross-section \(A\) is pushed along its length \((L)\) by means of a force of magnitude, \(F.\) There is no friction anywhere. Ignore the weight of the rod. The longitudinal stress in the rod, at a distance \(\dfrac{L}{3}\) from the left end, is:
1.
tensile, \(\dfrac{F}{3A}\)
2.
compressive, \(\dfrac{F}{3A}\)
3.
tensile, \(\dfrac{2F}{3A}\)
4.
compressive, \(\dfrac{2F}{3A}\)
Subtopic: Stress - Strain |
Level 3: 35%-60%
Hints
A simple pendulum is made with a thin wire (length: \(l,\) area: \(A,\) Young's modulus: \(Y\)) attached to a heavy bob of mass \(M.\) The pendulum is released from the rest with the bob at the same level as the point of suspension and swings down in a circular arc. The elongation in the wire when the bob reaches the lowest point is:
| 1. | \(\dfrac{3 M g l}{A Y}\) | 2. | \(\dfrac{2 M g l}{A Y}\) |
| 3. | \(\dfrac{3 M g l}{2 A Y}\) | 4. | \(\dfrac{M g l}{A Y}\) |
Subtopic: Hooke's Law |
Level 3: 35%-60%
Hints
A cube made of a homogeneous, isotropic elastic solid is acted upon by forces of equal magnitude acting perpendicular to its opposite faces as shown. Forces are applied uniformly over the area of each face. The stress at the centre of the cube is:
1. tensile
2. compressive
3. shear
4. zero
1. tensile2. compressive
3. shear
4. zero
Subtopic: Stress - Strain |
Level 3: 35%-60%
Hints
An extremely long solid rod of length \(L\) starts falling longitudinally towards a large point mass \(M,\) the near end of the rod being at a distance \(L\) from the mass \(M.\)
The rod experiences:
The rod experiences:
| 1. | no stress | 2. | compressive stress |
| 3. | tensile stress | 4. | shear stress |
Subtopic: Stress - Strain |
Level 3: 35%-60%
Hints
A large cylindrical piece of a dense solid elastic metal stands on its end as shown in the figure. The metal is uniform and isotropic. The stress in the material as a function of height is shown correctly by:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Stress - Strain Curve |
Level 3: 35%-60%
Hints
The block, shown in the figure, is suspended as shown from two identical steel wires. The extension in the wires due to the tension is \(\Delta l_1.\) If the block is suspended by one of the wires the extension in it is \(\Delta l_2.\) Then \(\dfrac{\Delta l_1}{\Delta l_2}\) equals:
| 1. | \(1\) | 2. | \(2\) |
| 3. | \(\sqrt 2\) | 4. | \(\dfrac12\) |
Subtopic: Young's modulus |
65%
Level 2: 60%+
Hints
A uniform rod \(AB\) is rotated at a constant angular speed about its end \(A,\) the rotation axis being perpendicular to \(AB.\) During rotation, stresses are set up in the rod. Let the stress at \(A\) be \(\sigma_A\) and that at the centre \(C\) be \(\sigma_C.\) Then:
1. \(\sigma_A=\sigma_C\)
2. \(\sigma_A=2\sigma_C\)
3. \(\sigma_C=2\sigma_A\)
4. \(\sigma_C=\dfrac34\sigma_A\)
1. \(\sigma_A=\sigma_C\)
2. \(\sigma_A=2\sigma_C\)
3. \(\sigma_C=2\sigma_A\)
4. \(\sigma_C=\dfrac34\sigma_A\)
Subtopic: Stress - Strain |
Level 4: Below 35%
Hints
An ideal gas has an isothermal bulk modulus of \(B_1.\) Its volume is doubled, isothermally. The bulk modulus is now:
| 1. | \(B_1\) | 2. | \(2B_1\) |
| 3. | \( \dfrac {B_1}{2}\) | 4. | \(\dfrac {B_1}{\sqrt 2}\) |
Subtopic: Shear and bulk modulus |
Level 3: 35%-60%
Hints
The breaking stress in two wires of different materials \(A,B\) are in the ratio: \(\dfrac{S_A}{S_B}=\dfrac12,\) while their radii are in the ratio: \(\dfrac{r_A}{r_B}=\dfrac12.\) The tensions under which they break are \(T_A\) and \(T_B.\) Then \(\dfrac{T_A}{T_B}=\)?
| 1. | \(2\) | 2. | \(\dfrac14\) |
| 3. | \(\dfrac18\) | 4. | \(\dfrac1{2\sqrt2}\) |
Subtopic: Stress - Strain |
72%
Level 2: 60%+
Hints
The elastic energy density in a stretched wire is:
| 1. | \(\text{(stress)}^2 × \text{strain}\) | 2. | \(\text{stress} × \text{strain}\) |
| 3. | \(\dfrac12\times \text{stress} × \text{strain}\) | 4. | \(\text{stress} × \text{(strain)}^2\) |
Subtopic: Potential energy of wire |
92%
Level 1: 80%+
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